In this section we explore a special operator class for which a number of spectral theory theorems can be applied. As an application of the obtained abstract results we study a basis property of the root vectors of the operator in terms of the order of the operator real part. By virtue of such an approach we express a convergence exponent of \( {\it s} \) -numbers through the order of the operator real part.
Bellow, we give a slight generalization of the results presented in [1]}.
